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Infinity
]] Infinity (symbolzed: ∞) is a term derived from the Latin infinitas or "unboundedness" denoting concepts involving limitless quantity, numeration, extension or expansion. In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as the real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e. a number greater than any real number. Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite. Quotes ]] ]] * If a thing loves, it is infinite. ** William Blake, in Annotations to Swedenborg (1788) * If the doors of perception were cleansed everything would appear to man as it is, infinite. ** William Blake, in A Memorable Fancy in The Marriage of Heaven and Hell (1790–1793) * To see a World in a Grain of Sand And a Heaven in a Wild Flower, Hold Infinity in the palm of your hand And Eternity in an hour. ** William Blake, in Auguries of Innocence (c. 1805) - Full text online * There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated. ** Georg Cantor, in "Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" the different views with regard to the actual infinite numbers" - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886) * Each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite. ** Georg Cantor, in "Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" the different views with regard to the actual infinite numbers" - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886) * The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great. ** Georg Cantor, in "Mitteilungen" (1887-8) * I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures. ** Georg Cantor, as quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by Rosemary Schmalz. * The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds. ** Georg Cantor, as quoted in Infinity and the Mind (1995) by Rudy Rucker *And in that moment, I swear we were infinite. ** Stephen Chbosky, in The Perks of Being a Wallflower (1999) * The primary Imagination I hold to be the living power and prime agent of all human perception, and as a repetition in the finite mind of the eternal act of creation in the infinite I AM. ** Samuel Taylor Coleridge, in [http://www.gutenberg.org/dirs/etext04/bioli10.txt Biographia Literaria (1817), Ch. XIII] External links Category:Themes